Questions: For f(x)=x+4 and g(x)=3x+3, find the following functions. a. (f ∘ g)(x); b. (g ∘ f)(x); c. (f ∘ g)(1); d. (g ∘ f)(1) a. (f ∘ g)(x)= (Simplify your answer.)

Transcript text: For $\mathrm{f}(\mathrm{x})=\mathrm{x}+4$ and $\mathrm{g}(\mathrm{x})=3 \mathrm{x}+3$, find the following functions. a. $(f \circ g)(x) ; b .(g \circ f)(x) ; c .(f \circ g)(1) ; d .(g \circ f)(1)$ a. $(f \circ g)(x)=$ $\square$ (Simplify your answer.)

Solution

Solution Steps

To solve the given problem, we need to find the compositions of the functions $ f $ and $ g $. Specifically, we need to:

Find $ (f \circ g)(x) $, which means applying $ g(x) $ first and then applying $ f $ to the result.
Find $ (g \circ f)(x) $, which means applying $ f(x) $ first and then applying $ g $ to the result.
Evaluate $ (f \circ g)(1) $ by substituting $ x = 1 $ into the composition found in step 1.
Evaluate $ (g \circ f)(1) $ by substituting $ x = 1 $ into the composition found in step 2.

Solution Approach